Worldwide Multivariable Calculus 1st edition

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• Chapter 1: Multivariable Spaces and Functions
  • 1.1: Euclidean Space
  • 1.2: ℜⁿ as a Vector Space
  • 1.3: Dot Product, Angles, & Projection
  • 1.4: Lines, Planes, and Hyperplanes
  • 1.5: The Cross Product
  • 1.6: Functions of a Single Variable
  • 1.7: Multivariable Functions
  • 1.8: Graphing Surfaces
  
  
• Chapter 2: Multivariable Derivatives
  • 2.1: Partial Derivatives
  • 2.2: The Total Derivative
  • 2.3: Linear Approximation, Tangent Planes, and the Differential
  • 2.4: Differentiation Rules
  • 2.5: The Directional Derivative
  • 2.6: Change of Coordinates
  • 2.7: Level Sets & Gradient Vectors
  • 2.8: Parameterizing Surfaces
  • 2.9: Local Extrema
  • 2.10: Optimization
  • 2.11: Lagrange Multipliers
  • 2.12: Implicit Differentiation
  • 2.13: Multivariable Taylor Polynomials & Series
  
  
• Chapter 3: Multivariable Integrals
  • 3.1: Iterated Integrals
  • 3.2: Integration in ℜ²
  • 3.3: Polar Coordinates
  • 3.4: Integration in ℜ³ and ℜⁿ
  • 3.5: Volume
  • 3.6: Cylindrical and Spherical Coordinates
  • 3.7: Average Value
  • 3.8: Density and Mass
  • 3.9: Centers of Mass
  • 3.10: Moments of Inertia
  • 3.11: Surfaces and Area
  
  
• Chapter 4: Integration and Vector Fields
  • 4.1: Vector Fields
  • 4.2: Line Integrals
  • 4.3: Conservative Vector Fields
  • 4.4: Green's Theorem
  • 4.5: Flux Through a Surface
  • 4.6: The Divergence Theorem
  • 4.7: Stokes' Theorem